john and mary are working on a job together. if john does it alone, it will take him seven days, while mary can do it alone in five days. how long will it take them to do it together?
john rate= job/7hrs
mary rate=job/5 hrs
combined rate= job/7hrs+job/5hrs= (5+7)/35= 10/35 job/hr
so, time= howmuch/rate= 1job/(10jobs/35hrs)= 3.5 hrs
Or, if you use base 10, where 7+5=12, that would be 35/12 hours, or 2 hours 55 min
The 3.5 hours caught my eye, because that would be the time taken by 2 people who take 7 hours each.
To figure out how long it will take John and Mary to complete the job together, you can use the concept of "work rates". The work rate of a person is the amount of work they can complete per unit of time.
Let's first find the work rates of John and Mary individually. If John can complete the job alone in 7 days, his work rate would be 1 job / 7 days, or 1/7 jobs per day. Similarly, if Mary can complete the job alone in 5 days, her work rate would be 1 job / 5 days, or 1/5 jobs per day.
To find the work rate of John and Mary together, we can add their individual work rates. So, their combined work rate would be (1/7) + (1/5) jobs per day.
To determine how long it will take them to complete the job together, we need to find the reciprocal of their combined work rate. The reciprocal of a quantity represents the amount of time required to complete one job.
Therefore, the time required for John and Mary to complete the job together is 1 / [(1/7) + (1/5)] days.
To simplify this equation, we need to find a common denominator for the fractions in the denominator:
(1/7) + (1/5) = (5/35) + (7/35) = 12/35.
So, the equation becomes:
1 / (12/35) = 35/12 days.
Hence, it will take John and Mary approximately 35/12 days (or approximately 2.92 days) to complete the job together.